With the growth of biological information, the efficiency of database retrieval has become central to the biological enterprise. In particular, one can change a retrieval method and must be able to evaluate whether the change is an improvement or not. Initially, using U-statistics, we developed central limit theorems describing the behavior of the receiver operating characteristic curve n (ROCn) under bootstrapping. Our methodology was applied to determine which changes to the PSI-BLAST program actually constitute improvements. Eventually, however, we rejected the ROCn as an unacceptable measure of database retrieval efficacy for bioinformatics, substituting in its place the TAPk. By measuring the retrieval efficacy for each query (which the ROCn cannot always do), the TAPk permits metrics on retrieval methods, to determine how closely related two retrieval methods are by their behavior query by query. The metrics can distinguish, e.g., a tweak on an accepted retrieval algorithm (which produces retrieval close to the algorithm's) from a truly novel algorithm (which produces a distant retrieval), thereby rewarding originality in bioinformatics, by objectively displaying incremental improvements of existing algorithms for what they are.